Transverse-field muon spin rotation measurements of overdoped La2-xSrxCuO4 reveal a large broadening of the local magnetic field distribution in response to applied field, persisting to high temperatures. The field-response is approximately Curie-Weiss like in temperature and is largest for the highest doping investigated. Such behaviour is contrary to the canonical Fermi-liquid picture commonly associated with the overdoped cuprates and implies extensive heterogeneity in this region of the phase diagram. A possible explanation for the result lies in regions of staggered magnetization about dopant cations, analogous to what is argued to exist in underdoped systems.
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